I like the general feel of (physical) combat the way it is, but there are a few tweaks that could definitely take it to the next level. I admit that the mechanics I favor may not be everyone's cup of tea, but I appreciate having the opportunity to throw some of my ideas out there to see what sticks with the devs and with the community. I expect to continue enjoying this game for years, and the chance to offer input on its growth is awesome.
First of all, let me get my gaming bias out of the way: the majority of my gaming experience (as a player and as a creator) comes from MUDs. I have also logged many hours playing TBS games, RTS games, RPGs, and console platformers, but I generally have no clue how the actual numbers of their combat systems work.
Combat in a MUD tends to be coded/designed as a one-on-one conflcit, which is how each attack in a tactical battle basically plays out, so I think that some of the combat systems from that world can be applied here.
My first observation is that it would definitely help to separate to-hit and to-damage rolls. When the game tells me that all 4 of my longbow archers missed a lumbering Drake or Troll two tiles away, I tend to say unkind things to my computer about how that's not entirely plausible. In that case, it's really more fun to be told that they hit for 0 damage than that they (all) missed. Also, it makes for some more variety in a battle when sometimes you miss (e.g., because you're shooting all the way across the screen), and sometimes you just don't hurt them (e.g., because their armor deflects the blow from your dagger). It also gives some depth to weapon selection if there is a trade-off between accuracy (to-hit) and attack strength (to-damage), and it opens up the issue of losing accuracy when a character with low strength tries to wield a heavy weapon (like a Claymore or war hammer) instead of just having a damage penalty. For that matter, it can give depth to armor because agility (based on the dexterity score, dodge bonuses from armor, combat speed, etc.) could impact accuracy as well as reducing your enemy's to-hit roll.
The second thing that jumps out at me, which I learned from designing weapons for MUDs, is that 1dX damage rolls aren't any fun for reasonably powerful weapons. Unfortunately, it's just too random, and players expect their sword with a nominal attack value of 12 to generally do something close to 12 damage. Since 1dX gives an equal chance of 1 damage as 12 damage, it tends to leave unhappy players. There are a couple of options to make this work better. To get X nominal damage, you could go with 1d(X/2)+(3X/4) to get a roll from 3X/4 to 5X/4 (75% to 125%, 9 to 15 for our sword that does 12 damage). That makes it a little bit better, but I think it is still too random.
A better plan would be to use multiple dice. This is one thing that made multi-weapon ships in GalCiv2 much more fun than ships with a single more-powerful weapon: they have much more consistent damage rolls because they're rolling NdX (where N is the number of weapons, and X is each weapon's nominal damage) instead of 1d(N*X). Also, if I recall correctly, this mechanic was used to balance multi-soldier units, so a squad in E:WoM 1.07 does 8dX damage. As for how to display this to the user, I would either quote a range (min and max if they're meaningful, inter-quartile range or possibly +/- standard deviation if that makes more sense) or the average. Going with NdX dice in a weapon (or NdX+B where B is just a to-damage bonus), I would just display the average on the UI where the maximum damage is shown now. This allows the actual dice (and therefore the distribution of the results for a given weapon) to be adjusted by the devs to get the best game balance without necessarily changing the nominal/average damage of the weapon.
As for defense, I would consider rolling something like 1d(3X/4)+(X/2) so that defense is randomly 50%-125% of the armor's rated defense value (or some other range that makes the game balance fun, even if that is simply 100% of the armor's rated defense value with no variation), but using multiple defense dice is definitely a viable solution as well if working with two normal distributions (and even more calls to the random number generator) is viable from a performance and design point of view. One big thing though is that late-game units either need to have fewer HP, or average attack rolls should be significantly higher than average defense rolls to keep late-game tactical battles from dragging on forever.
In this system, basically, a single attack (or counter-attack) would have the attacker roll to-hit (e.g., success if 1d100 < attacker's to-hit% stat; display "Miss!" on a failed roll), have the defender roll to-dodge (e.g., success if 1d100 < defender's dodge%; display "Dodged!" on a successful roll), and then roll for attack (i.e., damage) and defense (i.e., damage mitigation).
In my opinion, the best way to simplify all of this into a good UI for the player was suggested by Phazon88: display a tooltip when you mouseover an enemy unit showing your %chance of hitting and your average damage predicted for the attack. This could be near the cursor, or it could make use of the little box that already pops up to show terrain defense modifiers.
Thanks again for giving the community an opportunity for input on such a key part of the game. I look forward to seeing where you guys take it from here.
PS. I'm not sure if the E:WoM dice are [0,X) or [1,X], so please forgive any off-by-one errors in my math. 
PPS. I also apologize that this post got long-winded and a bit rambling. It's been a while since I thought much about combat mechanics, and I don't have the dice-roll analysis tool that I wrote on this computer, so I can't give any good multi-dice examples right now. If there is any interest, I could look at some potential damage dice for the game's current weapons another time.